Workshops organised by the project

The sight of new growth following a devastating forest fire shows nature’s inherent ability to withstand major disturbances and rebuild itself when necessary. Understanding how such complex systems demonstrate resilience by absorbing or recovering from major external perturbations allows scientists to learn valuable lessons. The multidisciplinary PATRES team will develop new methods defining the actions favouring the recovery from perturbations, applicable from ecology to cognitive sciences and sociology, in a project that will bridge the divide between the physical and social sciences.

Contents

Resilience

Complex systems are often capable of showing remarkable robustness. Despite major changes in their surrounding environment they are somehow able to adapt and survive by overcoming negative effects. Examples include bacterial colonies developing resistance to antibiotics, beaches recovering from oil spills, and human societies remaining intact even in the face of natural disasters and economic pressures.

Scientists and mathematicians have studied this type of resilience for over thirty years. After all, the ability of a system to absorb or recover from disruption is just as important as its performance under more favourable conditions.

Methods for modelling such resilience are far too simplistic, making it difficult to discover the key to this robustness. By uniquely combining viability theory and the mathematics of pattern dynamics, the PATRES project will develop new modelling techniques. The team will demonstrate that abstract maths has many practical applications, ranging from the sustainable use of African Savannah to improved business networks.

Currently, models of resilience in complex systems presume that such systems will eventually reach a state of equilibrium following a perturbation. This focus on maintenance and recovery is a long way from reality, however, as occasional changes in the environment can cause a dramatic shift to another state resulting in entirely new behaviour patterns.

A viable approach

Work recently undertaken at the Agricultural and Environmental Engineering Research Institute (Cemagref) in France suggests that drawbacks to the current models may be overcome by employing viability theory. By ignoring the mechanisms behind a system’s resilience, this approach is able to look at the effort or ‘cost’ required for maintaining or restoring particular functions of a system during disruption. The cost can be translated as a quantitative measure of a system’s robustness.

Unfortunately, this method has one major drawback; the intricate viability calculations need significant computer resources. In practice, therefore, this promising approach can only cope with relatively small systems, certainly not the levels of complexity found in most ecological, biological or societal systems.

The PATRES project is seeking ways to overcome these limitations and establish viability modelling as an effective way to study resilience. The project’s coordinator, the Laboratory for Complex System Engineering within Cemagref, has brought together a multidisciplinary team of researchers with this particular aim in mind. They will join forces to develop methods to ‘simplify’ the complex systems, construct viability models, and test their ability to simulate and predict outcomes for real-world situations.

Patterns for partnership

Several of the project partners have a particular interest in the mathematics formation and recognition. It is impossible for viability models to work for systems with a large number of interconnected agents. But where the interconnections have statistical regularity or ‘patterns’, the complexity can be diminished. Rather than trying to describe the agents and their interactions, you describe the patterns they make instead.

Although the bulk of PATRES deals with highly abstract and advanced mathematics, the partners will apply their collective knowledge and experience to develop two complementary software types. The first is a tool for identifying and modelling patterns and their dynamics in complex models. The second will compute the resilience properties of a system and determine what kinds of action are required to maintain or restore the patterns within it.

The partners will use the software tools to explore resilience in very different complex real-world systems. These may include producing models, which can be applied to the learning of sequences in basal ganglia. The tools will also help to solve practical problems in a number of other areas such as bacterial dispersion biofilms (to improve water treatment technology), the sustainable management of trees and grass in savannah landscapes (to conserve biodiversity and identify sustainable stocking rates).

These tools can also be used to study the emergence and demise of language in human societies, thus aiding the identification of policies that can help preserve languages that are under the threat of extinction. The work can also be applied in business to study the strength of networking structures between biotechnology firms, and how successful networks are cushioned or recover from major economic upsets.

The wide-ranging applications of the novel modelling techniques and software highlight the importance of this project to Europe’s capabilities in resilience research. The project involves researchers specialised in physics, ecology, social sciences, cognitive sciences, computer sciences and applied mathematics, making the new tools and techniques potentially highly flexible and easily adopted by scientists from many other disciplines.

The work to test PATRES’ methods in five specific case studies will disseminate the results of the project to a much wider research community.

Summary of Objectives

The project objectives are:

to develop new methods and tools for defining synthetic (i.e. in low dimensions) descriptions of complex dynamics, based on robust pattern dynamics,

to develop new methods and tools for defining action policies in order to maintain or restore desired pattern dynamics in a complex system,

to test and illustrate these innovations on a set of case studies.

The project will develop methods and prototype software tools for modelling and managing pattern resilience in complex systems. Pattern resilience is understood as the capacity of the system to maintain or to recover some desired pattern dynamics (which are related to useful functions) in a changing environment. The pattern dynamics are evolving statistical regularities which are generated by the interconnected components of the system. We shall build on statistical physics and Pattern Oriented Modelling techniques to develop a set of robust techniques to express such pattern dynamics in state spaces of relatively small dimensionality. Viability theory will provide a framework for an inclusive, rigorous and practical definition of resilience, which give possibilities to find sets of actions to maintain or restore the satisfactory pattern dynamics in a system.

Applications

Bacteria dynamics

Land-use in semi-arid Savannas

Learning sequences in basal ganglia

Language dynamics

Biotech firm networks

The project will test its methods and the software tools on a set of concrete applications, in collaboration with field specialists. It will build on the tests to refine and improve the methods and tools. The applications include: bacteria dynamics, land-use in semi-arid savannas, learning of sequences in basal ganglia, language competition, biotech firm networks. We expect the use of these new methods to bring new knowledge about the resilience of these systems.